Note: The author is grateful to the editor and to two anonymous referees for their helpful comments. In addition, this paper has benefited from seminar participants' suggestions at Goethe University, the RGSE conference in Duisburg, the IAES conference in Istanbul, and the meeting of the Verein für Socialpolitik in Göttingen.
Parametric Lorenz Curves and the Modality of the Income Density Function
Version of Record online: 30 JUN 2013
© 2013 International Association for Research in Income and Wealth
Review of Income and Wealth
Volume 60, Issue 4, pages 905–929, December 2014
How to Cite
Krause, M. (2014), Parametric Lorenz Curves and the Modality of the Income Density Function. Review of Income and Wealth, 60: 905–929. doi: 10.1111/roiw.12047
- Issue online: 9 NOV 2014
- Version of Record online: 30 JUN 2013
- goodness of fit;
- income distribution;
- Lorenz curve;
Similar looking Lorenz curves can imply very different income density functions and potentially lead to wrong policy implications regarding inequality. This paper derives a relation between a Lorenz curve and the modality of its underlying income density: given a parametric Lorenz curve, it is the sign of its third derivative which indicates whether the density is unimodal or zeromodal (i.e., downward-sloping). The density modality of several important Lorenz curves such as the Pareto, Weibull, Singh–Maddala parametrizations and hierarchical families of Lorenz curves are discussed. A Lorenz curve performance comparison with Monte Carlo simulations and data from the UNU–WIDER World Income Inequality Database underlines the relevance of the theoretical result: curve-fitting based on criteria such as mean squared error or the Gini difference might lead to a Lorenz curve implying an incorrectly-shaped density function. It is therefore important to take into account the modality when selecting a parametric Lorenz curve.